Critical behavior of ion mobilities near the superfluid transition

Measurements are reported of the mobilities of helium ions in superfluid helium very close to the $\lambda$ transition. The mobilities of both positive and negative ions appear to be singular in the sense of having infinite slope at the transition. The measurements are made by a new differential technique, based on the space-charge-limited method, which makes possible a sensitivity to changes in mobility of the order of parts in ${10}^4$. This allows mobility measurements into the range $\left|\epsilon \right|<\mathrm{}{10}^{-4\mathrm{}}$, where $\epsilon =\left(\frac{T}{T_{\lambda }}\right)-1\mathrm{}$. Most of the reported measurements are taken along isotherms which cross the $\lambda$ line at elevated pressures, although a series at saturated vapor pressure is also reported. Means of transforming the data between various thermodynamic paths are discussed. Uncertainty as to which thermodynamic path should be considered fundamental together with experimental problems in the technique at this stage in its development make quantitative assessment of the singularity difficult. However, if we assume a limiting form $\frac{(\mu -{\mu }_{\lambda })}{{\mu }_{\lambda }}\sim {(-\epsilon )}^{{\rho }^{\prime }}$, where $\mu$ is the mobility and ${\mu }_{\lambda }$ its value at the transition, we find for the exponent ${\rho }^{\prime }=0.94\mathrm{}\pm 0.02$.